Tag Archives: Paul Erdos

Networks; The Power of Hubs

How do some  webpages on the Internet become so ubiquitous that we are rarely ever less than two short links away from viewing that page? How have some webpages become so popular among the hundreds of billions of webpages that are on the Internet currently, not to mention the new ones that pop up almost every second? More importantly how do certain pages become the centre for web activity and lead us to other pages within their network? Albert-Lázló Barabási explored these questions about networks and the organization/disorganization of interconnectivity within his Chapter titled Hubs and Connectors .

Barabási begins the piece by explaining both the power and importance of links within the web. Quite simply the larger number of Continue reading

He has Connections… How can I get to know Him!!? Network.

The reading for this week, Linked by Albert-Laszlo Barabasi disproves the idea of randomness in networks and champions the idea of hubs and connectors that function to bring together society. The idea behind linked and being connected to others is not new nor is it phenomenal: it is in our blood. This is our history and thus, inevitable. The Bible clears demonstrates this connection as in the beginning, there was Adam, then Eve, then Cain and Able. After that, humanity arises and creates towns to settle and we develop. Thus, we are all connected or linked in some way. If one is agnostic or believes in science, then think of evolution. People evolved as running from animals to hunting them in groups. Once in groups, they became nomads, and then quite surely, someone decided to settle down in a location, therefore forming a town. Thus a hub is created and with it, streets, other towns, etc…

It is divided into 3 chapters. I will discuss each chapter separately by its part and tie it together at the end. They are all connected; rather, they are components of a larger truth.

The Fifth Link: Malcolm Gladwell’s The Tipping Point notices an interesting phenomenon: “sprinkled among every walk of life…are a handful of people with a truly extraordinary knack of making friends and acquaintances. They are connectors” (55). This brings in the idea of connectors as highly relevant components of our social lives. Another way to define connectors is by calling them hubs. These hubs have a large number of links. One can create the analogy of a large city, such as Los Angeles and the suburbs that surrounds it. Many highways enter and go out of Los Angeles, connecting many different cities along the way. This discovery has basically disproven Erdos-Renyi’s theory of random worldview and Watts and Strogatz’s simple circle network model. Social networks exhibit clusters and hubs, both points that demonstrate a worldly rule that applies.

We can also apply the theory of links and connectors/hubs to cyberspace. The World Wide Web is the ultimate space for freedom, an environment that represents and defines the meaning of space without limits, boundaries, nor rules. Anyone can publish their work online and allow anyone to see it. Problem is, there are billions of websites. The question that arises is visibility. On the Web, the “measure of visibility is the number of links. The more incoming links pointing to your Webpage, the more visible it is” (57). As such, only websites that become hubs are highly visible (Amazon, Google). These are hubs: connectors with enormous links to other nodes.

I can create a website, thus it becomes a node. Google has grown, thus it has become a hub. Without a link, both websites exist and move in different worlds, or just space. The internet is as big as the universe, each node moves on its own, until it makes contact. This is the link. My website can function in its own galaxy as networks tend to form a cluster. Clusters are “nodes that are linked only to nodes in their subculture or genre” (61).  As a cluster, it is easier to find a common connection to a hub. For example, if my website is about knee pains, then I would like to create some link to a popular website such as WebMD. This in turn, can allow me to link with Google. In two links, my website has escaped randomness and can be visible.

The Sixth Link: Vilfredo Pareto may be a well known Italian economist, but I feel that his thought process behind the 80/20 Rule is sheer brilliance. It is all around us, and yet, he is the first to notice that it applies to the world. This is Simple Genius: understanding a law within the world that is so visible, and yet, invisible to the eye. 80/20 Rule applies to many things, but is generally regarded as 20 own rest of the 80. This also applies to network as well. It can be proven through a mathematical expression called a power law. In contrast to a bell curve, which is a “distribution rather similar to the peaked distribution characterizing random networks,” (67) the power law is by definition a special kind of mathematical relationship between two quantities. The exact definition is as follows: if one quantity is the frequency of an event, the other is the size of the event, then the relationship has a power law distribution when the frequency of the event decreases at a greater rate than the size increases. In layman terms, think of 20% of the population ruling 80% of the world.

Power laws basically functions to prove mathematically the fact that in most “real networks the majority of nodes have only a few links and that these numerous tiny nodes coexist with a few big hubs, nodes with an anomalously high number of links” (70). Again, this relates to Gladwell’s idea of connectors, but proving quantitatively that it exists within the realm of the World Wide Web. It demonstrates that real networks are not random at all, but exist under the power law. The interesting idea that Barabasi proposes is that in the beginning, nodes tend to be chaotic and without any form or order. However, through time, this disorder turned into order through self-organization. Under the theory of phase transitions, real networks demonstrate self creation from disorder into the 80/20 Rule. Barabasi’s idea is highly compelling, as he demonstrates quantitative analysis and by using the Web, a blank space which is like a universe unto itself, to explain a simple law that applies to the world. Everyone is intricately linked, because we are social beings. Networking is only a function of humanity, which always existed, but has now been proven through the power law. A question that arises is why do hubs and links form and how does it form in such a manner that to the naked eye is so random and chaotic, and yet, has order.

The Seventh Link: Erdos and Renyi’s model of networks rely on two principles. First is the idea that all nodes are fixed and remains unchanged throughout the network’s life. Second is that all nodes are equivalent. However, this is obviously not the case as there exists hubs/connectors, links, and change from disorder to order through self-organization. To understand how it does this, we must understand that the web is constantly growing. It is changing and growing. This is quite self-explanatory. There has been exponential growth of websites on the World Wide Web. As there is growth, we can safely disprove the static nature of Erdos-Renyi’s model of networks. We also do not randomly decide on which websites to link. We choose based upon our knowledge and social upbringing. We prefer certain websites over others because we are comfortable and familiar with that certain product. Thus, rises the concept of hubs. Barabasi brings up the idea of preferential attachment: “when choosing between two pages, one with twice as many links as the other, about twice as many people link to the more connected page. While our individual choices are highly unpredictable, as a group we follow strict patterns” (85). In many sense, this is true. We are all sheep and follow the leader.

In truth, randomness does not really exist unless it is the role of a die. Linking between networks is not random. Though unmentioned as third criteria, I believe that popularity and attractiveness plays an important role in the addition of links and creation of hubs. Webpages that have more links are more likely to be “linked to again” (86). Thus, there exists first person advantage. Older nodes have greater chances to become bigger and eventually rise as a hub. As a senior member within a link, this node has greater links and more nodes want to be linked to that certain node. Barabasi has given compelling evidence that real networks are not random, but constantly evolving and growing, attracting more links through the legitimacy of the power law.

We are living in a complex world and yet, guided by the invisible hand or law that is, in my opinion, inexplicable. The idea of real networks applies not only to websites, but to humanity in large. I believe that Barabasi’s point is that humans are social beings and we are followers. There are different people: some are leaders and some are followers. This difference guides the principle of 80/20 Rule as well as the power law. Barabasi has done something quite remarkable: take a simple, obvious, and yet invisible rule, and proved it scientifically and gave it a name. Kudos.

All Linked Up: An analysis on the growth of networks.

Our latest reading is Linked written by Albert-Laszlo Barabasi. The reading centers on research and developments regarding the “network” through time.

  • The reading describes how network analysis originally grew from graph theory. Leonhard Euler, was a Swiss mathematician who first examined graph theory. Euler addressed an issue in a small town called Konigsberg where locals wanted to discover if there was anyway one could, “walk across the seven bridges and never cross the same on twice?” Euler discovered that such a method did not exist by constructing a graph based on the bridges of Konigsberg, he made the various bridges nodes and connected them by links and thus the “network” was born.
  • Linked illustrates a network with the example given on page 14, if you gather a group of 100 strangers, then eventually as human beings have a natural desire for companionship, they’ll begin to form small groups of acquaintances. Then by introducing a small detail to the group, such as a rare wine, the news will rapidly spread by individuals or nodes that bridge the information from one group to another. Types of networks include the society, the internet, a cell, or the brain. And all these networks can be illustrated by graphs.
  • Paul Erdos and Alfred Renyi, two mathematicians who studied the wine simulation suggested the best way to form a network is to connect nodes randomly. By randomly connecting nodes, one will be eventually left with one giant cluster. Where in, one can navigate to anyone else by the navigating the links of the nodes. Similarly, one can say that all humans are apart of a worldwide social cluster, where we can navigate to one another through various connections. Nevertheless, Erdos and Renyi’s theory only takes into account random networks, where all nodes are equal. On the contrary, in the actual society web, networks have distinct class systems such as governments and social hierarchies.
  • Later on, Stanley Milgram, would reveal research that suggests that nodes in a network are less random than Erdos and Renyi thought them out to be. Milgram sought to find the “distance” between any two people in the United States and thus formulated an experiment where he sought to bridge two people by sending letters to randomly chosen residents. If you didn’t know the actually recipient, you would resend the letter to someone who you think might be closer to the recipient. Milgram’s research concluded the famous, “6 degrees of separation.” Similar to six degrees of separation, social networking websites such as facebook, and Myspace list mutual friend lists that illustrate this exact theory. When becoming friends with a NYU student from a different hometown then you, sometimes you’ll find that you’re already connected by a mutual friend. I just discovered that Emma now dorms with a girl who lived down the hall from me last year.
  • A current event that illustrates the six degrees of separation model is the new addition of “lists” to Twitter. Twitter, a social networking website has recently launched Twitter Lists which allows you to cluster users who have similar tweeting topics. Thus one can create, an athlete list, a movie star list, etc. Then people can subscribe to your lists to access the people you follow. So if one is looking for a very funny twitter user whom they don’t know, they might access their friends “Hilarious People List” and continue on the chain until they find exactly who they’re looking for. The new development was designed specifically for people who seek to make Twitter more organized. http://blog.twitter.com/2009/09/soon-to-launch-lists.html
  • Moving along, in 1980 Tim Berneres-Lee sought to make the information in every computer accessible to everyone else, Tim envisioned a virtual network where we all bridge to one another, and this network eventually became the World Wide Web. This made me recall a previous post on our blog called, “The Power of Words,” (https://idm09.wordpress.com/2009/10/04/the-power-of-words/) the post discusses how society has taken technologies from the past and built upon them to apply them to the needs of today. It’s easy to see how networks have grown from groups of immediate neighbors, to long-distance neighbors through postage, to the telephone network, to the internet. Through today’s World Wide Web, we’re allowed to stretch our networks farther than ever before because we correspond to virtually anyone in a matter of seconds. The post also describes how society needs links to help bind and restrict data, because too much data at one time would be overwhelming. Similarly, we need networks to better organize the people we know. Networks help us narrow down the people we know because taking on everyone can be overwhelming. Precisely what the new Twitter Lists are trying to accomplish.
  • Linked later goes on to describe how “six degrees” is a product of our modern society that we have designed to keep in touch or in other words communicate over long distances. In Mark Granovetter’s Social World he describes a network where small fully connected circles are connected by strong ties. Granovetter’s theory suggests that certain nodes can group together that bridge to another group by one link. When thinking about connections like that I recall, Zoom, the picture book by Istvan Banyai. In the book, the pictures unfold as if one is zooming in onto a specific image. Though certain pictures are connected very tightly, they eventually connect to a transition picture that connects them to the next scene.
  • The last network discussed is the Circle Network by Duncan Watts and Steven Strogratz. Their networks illustrates how nodes are connected to immediate neighbors which are eventually connected through long range links. Unlike the previous networks, the Circle Network is not based on random bonds. It has the most structure, it’s very much like a classic character web in literature. Especially in Shakespearian literature, the characters have very distinct connections and relationships that play into a plot. This also shows how a “network” is an integral part in telling a narrative similar to how we’ve made other connections between narratives and media.

It’s a Small World After All

The reading for this week, Linked by Albert-Laszlo Barabasi, began to outline the concept of networks by highlighting several network theories.

The idea of networks first originated with a Swiss mathematician named Euler.  He lived near a town named Konigsberg which had seven bridges.

The people of the town had always tried to cross all the bridges only once, but Euler offered a proof that it was impossible to cross the seven bridges of Konigsberg without crossing one more than once by laying out vertices at common points.  This spurred the idea of graph theory, which includes “a collection of nodes connected by links” (11).  His graph had nodes that were pieces of land and links that were bridges.  Nodes with an odd number of links must either be the start or end of the journey, and since the graph had more than 2 nodes with an odd number of links, there was no way to only cross each bridge once.

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